"Henri Cartan; Researcher Helped Revolutionize Math," by Martin Weil. Washington Post, 24 August 2008, page C7.
"Henri Cartan." The Telegraph, 24 August 2008.
"Henri Cartan, French Mathematician, Is Dead at 104," by Kenneth Chang. The New York Times, 25 August 2008.
"Henri Cartan: Distinguished French mathematician and member of Bourbaki," by Ian Stewart. The Guardian, 1 October 2008.

Henri Cartan, one of the leading mathematicians of the
20th century, died 13 August 2008, at the age of 104. He was the
son of mathematician Élie Cartan and was one of the
founding members of the Bourbaki group. The group helped revive
French mathematics after World War I and put many mathematical
subjects on a firm logical foundation. Cartan was also famous for
co-authoring Homological Algebra with Samuel Eilenberg. He received the Wolf Prize in 1980, was a fellow of many national academies, had two students win the Fields Medal, and two others receive Nobel Prizes. Cartan was also known for his work in human rights and for helping re-establish contact between French and German mathematicians after World War II. Chang concludes his article with a quote from Jean-Pierre Serre about Cartan: "All by himself he put the level of French mathematics much higher." More about Cartan is in "Interview with Henri Cartan," written by Allyn Jackson, in the August 1999 issue of Notices.

According to a new study, the mathematics test scores of a child at age ten are most influenced by the mother's education, the home learning environment, and the quality of the preschool and primary school attended. These factors outweigh socio-economic influences, prompting researchers to recommend universal preschool as having benefits outweighing the potential costs. Previous work by the authors of the new study indicated that providing one year of preschool influences mathematical achievement in later years as much as a US$19,000 increase in family income. This research was based in England, where the typical child attends 18 months of preschool part time. By interviewing parents of over 2500 preschoolers, researchers established a standard of measurement for the "home learning environment (HLE)" and found that the influence of the HLE on a child's mathematical achievement at age 10 was second only to the mother's education (which was twice as influential as the father's education). As the article states, "This indicates that what parents do is as important as who they are."

"The tennis world was turned upside down Thursday when Coin stunned the No. 1 seed, Ana Ivanovic. Coin won 6-3, 4-6, 6-3 in the second round. Never before in the 40-year Open era had a top women's seed lost so early." The dramatic upset of the 2008 U.S. Open Tennis Tournament was reported all over the media, and the winner of the match, Julie Coin of France, seemed as surprised as anyone. Cohen's AP piece, picked up by CBS Sports, Yahoo Sports, and elsewhere, reports that Coin "spent much of the year playing in minor league events and nearly got knocked out of the Open qualifying. [She] recently played so poorly she thought about giving up the sport and relying on her mathematics degree from Clemson."

The segment reports on a mathematics class at the University of Colorado Denver that used many variables and a huge amount of data to come up with a plan that contributed to an efficiently organized Democratic National Convention held in late August. Matt Nabidy, who is pursuing his Ph.D. in mathematics at UC Denver, describes how the class used data to figure out 1) how to organize 21,000 volunteers, 2) how to design a bicycle-sharing system for the convention delegates (with 1,000 bikes available), and 3) how to assign space for the various competing events over several days. The team modeled how many volunteers would be needed, where they would be needed, and what tasks they would need to handle at what times. The reporter concludes, "as politicians, delegates and friends of delegates pedal their way to the evening speeches, most of them won't even realize they are riding on a foundation built of math." [Professor Harvey J Greenberg taught the Math Clinic and has posted .]

In a 2006 Business Week cover story entitled "Math Will Rock Your World," Stephen Baker wrote about how "with the rise of new networks...all of us were channeling the details of our lives into vast databases... Those with the tools and skills to make sense of them could begin to decipher our movements, desires, and shopping habits---and predict our behavior." Baker has now written a book on the subject, The Numerati, in which he "introduces us to the mathematical wizards who are digging through our data to decode us as patients, shoppers, voters, potential terrorists---even lovers." This article is an excerpt from a chapter called "The Worker."

In this excerpt, Baker introduces us to Samer Takriti, a mathematician at IBM, who is leading a team of Ph.D.'s tasked with mathematically modeling each of IBM's 50,000 tech consultants so that they can be utilized most efficiently. In Baker's words, Takriti's job is "to start optimizing his co-workers." Except for personnel files, Takriti's team has access to a large amount of information about each consultant, including resumés, online calendars, emails, and the use of cell phones and handheld computers. These provide information about each person's skills and experience, how they use their time, their movements, and their social networks. If Takriti is successful, a manager could sit down at a computer, and, by filling out a simple form, she could compile a team who has the skills and abilities to quickly accomplish a particular task within budget anywhere in the world. And that's just one way such a system could be used.

In 2011, California will begin requiring algebra for its eigth-graders. This front-page article includes predictions about the consequences of the requirement and tries to explain that algebra is more than the calculations people remember from their school days. Several applications that are based on algebra are given in the article---such as Internet search engines, cell phones, and iPods---as are examples of how people use algebra in their jobs. Quotes about the subject from mathematicians and non-mathematicians (including California Governor Schwarzenegger) run in the article and in a section accompanying it. Keith Devlin (Stanford University) says that he would like to see mathematicians visit schools to show students the "cool side of mathematics." Devlin adds that "At any age, we will take the drudgery as long as we see a reason to do it." Tucker includes an excerpt from a 2002 essay (A Mathematician's Lament, a 25-page pdf) by former University of California, Santa Cruz mathematician Paul Lockhart: "If I had to design a mechanism for the express purpose of destroying a child's natural curiousity and love of pattern-making, I couldn't possibly do as good a job as is currently being done, ... I simply wouldn't have the imagination to come up with the kind of senseless, soul-crushing ideas that constitute contemporary mathematics education."

Russian mathematician Arkady Volozh is now the chief executive and one of the founders of Yandex, Russia's most popular search engine, a company valued at £2.5 billion. Volozh, who has a degree in applied mathematics, worked at "a Soviet state pipeline institute" when small private businesses were legalized in 1987, and then "was unexpectedly ordered to start dabbling in business." He quotes his boss as saying "you guys are mathematicians, you start a business." He started by trading computers and becoming technical director, then co-founded a company that became one of the largest distributors of computer technology in Russia. From there he co-founded Yandex "(short for yet another index), an engine aimed at improving Russian-language searching, which is complicated because of the grammar." While the company is very successful and profitable, Volozh does not flaunt his wealth and does not indicate interest in selling the successful venture.

This brief piece reports on new work by University College London researchers, who compared numerical abilities of children from two different cultures: from Australian aboriginal tribes, and from the city of Melbourne. Although the language used by the aboriginal people lack words for numbers, the two groups of children performed equally well on numerical tasks set for them by the researchers. "What we've shown is that we're born with a mechanism for seeing the world in number," researcher Brian Butterworth was quoted as saying.

Those few people possessing both a doctorate in mathematics and hands-on experience with the U.S. public education system are flush with job offers in mathematics education. However, the modal starting salary of only US$45,000 toUS $50,000 provides little incentive to obtain such a range of experience. Over half, or "60% of 128 tenture-track academic job advertised last year in mathematics education went unfilled," and few doctoral degrees in math education are available to help increase the pool of talented applicants. The article cites "Jobs in Mathematics Education in Institutions of Higher Education in the United States,", by Robert E. Reys (Notices of the AMS, June/July 2008).

Anyone who's been fortunate enough to have had experience with committee work has probably noticed that committees with many members are often inefficient. In fact, in the 1950s a British historian, C. Northcote Parkinson, found a "coefficient of inefficiency" at about 20 members. Researchers in Austria have used mathematical models to justify that number. They found that consensus is possible with 10-member committees, but becomes less likely as the committee grows. At 19-21 members, the number of ways not to reach consensus grows significantly. The European Union has 25 member states, but would like to reduce the number of commissioners to 18, which this research indicates would probably be a good idea.

Imagining four-dimensional objects is challenging. It can be done by looking at how three-dimensional objects can be viewed in a two-dimensional world, then extending the example to viewing four-dimensional objects in a three-dimensional world. Étienne Ghys of the École Normale Supérieure, in collaboration with graphic artist and engineer Jos Leys and mathematics graduate student Aurélien Alvarez, has created a series of videos to help the viewer imagine higher dimensions. Two familiar techniques are used: looking at "slices" of the five Platonic solids as they move through a plane or viewing the outline of the edges of these solids on a plane, then applying these techniques to the six regular four-dimensional objects. Ghys also applies a third technique called "stereographic projection," which Rehmeyer describes in this way: "Take a three-dimensional object, say a tetrahedron, and imagine pumping it up with air until it forms a perfect sphere with lines on the surface showing where the edges of the tetrahedron were. Now imagine putting the tetrahedron-sphere on a table, making it transparent, and putting a light bulb at the 'north pole.' The light would project patterns from the tetrahedron-sphere onto the surface of the table." See the videos, which include these stereographic projections as well as images of complex numbers and fractals.

"Chinese math students believe destiny is in the numbers," segment by Tom Brokaw. NBC Nightly News, aired 20 August 2008.

In this spot on NBC Nightly News (aired on television during the 2008 Summer Olympics held in Beijing), journalist Tom Brokaw notes that in China there is a mandate for junior high school children to take biology, chemistry, and physics, while in the U.S. only 18 percent of students elect to take those subjects. Chinese students pursue higher-level math and science at a much higher rate than in the U.S., as proficiency in the sciences is seen as a way to get a job and as a way to become an entrepreneur. Andrew Yao, who currently teaches at the Institute for Theoretical Computer Science, Tsinghua University in Beijing, expresses worry that young Chinese will go where the payoff is instead of going into pure science research. The streaming video of this segment is posted on the NBC Nightly News website.

"Spencer Peak added to Colorado mountain lexicon," by Howard Pankratz. Denver Post, 18 August 2008.
"San Juans peak named in honor of local activist," by Will Sands. Durango Telegraph 28 August 2008.

The U.S. Board of Geographic Names has designated a 13,087-foot mountain peak in Colorado "Spencer Peak," named after mathematician Donald Clayton Spencer, for "his outstanding national and international reputation and his popularity among the residents of southwest Colorado." Spencer received the prestigious Bôcher Prize from the American Mathematical Society in 1948, was elected to the National Academy of Sciences in 1961 and to the American Academy of Arts and Sciences in 1967, and was awarded the National Medal of Science in 1989 "for his original and insightful research that has had a profound impact on 20th-century mathematics and for his role as an inspiring teacher to generations of American mathematicians." He taught at Princeton University, where he was a mentor to John Nash. Spencer Peak is accessible by the Colorado Trail, south of Silverton and west of U.S. 550. See Spencer's obituary, "Donald C. Spencer, 89, Pioneering Mathematician, Dies," by Sylvia Nasar, in the New York Times, 1 January 2002.

Jacques Stern is a mathematician who turned to cryptography research and now heads the Laboratory of Computer Science at the Ecole Normale Supérieure in Paris. In this question-and-answer interview, Stern describes two main advances in cryptography that protect today's commerce: the concept of a public key system, devised by Whitfield Diffie and Martin Hellman, and RSA, which is a public key system currently in use today. RSA was developed by Ronald Rivest, Adi Shamir, and Leonard Adelman. RSA is based on the difficulty of factoring numbers that are products of large prime numbers. Stern said in the interview that recently a new system that uses multivariate algebra instead of number theory was under consideration in Europe as an alternative to RSA. "Our group broke it wide open last year and it had to be abandoned," Stern remarked. "That was extremely rewarding, because we prevented future disasters."

"Why do erudite people boast of blissful ignorance of maths?", by Donald Clarke. Irish Times, 16 August 2008.

In response to both an increase in the number of students failing math exams and the number of educated people who proudly claim they don't know math, the author poses the question of why this is so. He notes that these same individuals would never proudly claim they couldn't read or were ignorant of classic literature, and he bemoans what the future holds. "These innumerate dunderheads are going to have to build our bridges, design our trains and formulate our pharmaceuticals... The impending crisis for industry is worth fretting about, but one wonders why so few seem to care that a generation is being denied (or is denying itself) the illumination and intellectual excitement that comes with understanding mathematics. Like the Irish language and romantic poetry, math is, surely, worth studying for its own sake."

Monastersky writes about people who don't know much about a field but who still insist that they have made a great discovery, such as the person who wrote 33 physics professors about his discovery that "God's language is CRYPTOGRAPHY, which reveals that Global Warming is the end of the world." Underwood Dudley, professor emeritus of mathematics at Depauw University, has written two books on mathematical "crackpots," Mathematical Cranks and The Trisectors. His advice to researchers on how to discourage this type of communication is not to be too gentle with them: "Try to get them to quit, throw their stuff away. Tell them there's a federal law against this stuff, and if they don't stop, they'll be thrown in jail. Anything to get them to quit."

"Madison High teen known for his brilliance in math wins US$50K scholarship," by Laura Bruno. The Daily Record, 14 August 2008.

Akhil Mathew is one of five U.S. high school students to be awarded a US$50,000 Davidson Fellows Scholarship for his award-winning project, "Translation--Invariant Binary Representations." The 16-year old will be working on a graduate-level independent study project at Drew University starting this September. Mathew excelled at math from the time he was in grade school. His parents and teachers found him tutors and enabled him to take courses at Drew, where "he now assists two professors with a textbook by proofreading drafts, drawing the figures, formatting the text and creating a companion Web site." Alan Candiotti, a math professor at Drew, says "I've been teaching math for 35 years and [Akhil] is certainly the best. No one comes even close." Mathew's goal is to become a math professor at a major research institution, but in the meantime he continues his studies and volunteers to teach children chess at the Madison Public Library.

"Canadian Mathematicians, Grad Students to Fight AIDS with Numbers," from a Canadian Press news release. Macleans OnCampus, 13 August 2008.

This summer, a group of Canadian graduate students and mathematicians traveled to Botswana to attend the first MITACS Canada-Africa Biomath Network Summer School in Mathematical Biology. Their purpose? To learn more about the mathematical models that are used to understand and predict the spread of infectious diseases, including HIV/AIDS, malaria, and tuberculosis. According to the summer school web site, the two-week program consisted of lectures and tutorials and provided attendees with the opportunity for hands-on and computer work, as well as participation in group projects. The program was sponsored by the Canadian research network known as Mathematics of Information Technology and Complex Systems (MITACS) and the South African Centre for Epidemiological Modelling and Analysis (SACEMA).

Professor Arvind Gupta, scientific director of MITACS and one of the summer school organizers, stressed the importance of these models. "[They are] very important for health officials, because they need to figure out which groups they should target to stop the disease from spreading." University of Manitoba professor Abba Gumel, another summer school organizer, noted that the ease of international travel has made programs like this necessary: "We cannot just say we're sitting here in Canada, we don't care about what's going on elsewhere."

About four decades ago Russian physicist Victor Veselago theorized that it should be possible, using the proper materials in the right conditions, to create negative refraction, which would cause light waves to bounce backwards. This light-deflecting technique could one day be used to create "invisibility cloaks" around objects. The main challenge until recently has been that scientists couldn't build structures that were small enough to play these tricks on light. But combining sophisticated techniques from materials science and nanotechnology, two teams of scientists in the laboratory of Xiang Zhang, at the University of California at Berkeley, have made breakthroughs in the exciting area of metamaterial science, which attempts to create structures that manipulate light waves. One of the teams, led by graduate student Jason Valentine, was able to reverse near-infrared light. The other, led by graduate student Jie Yao, created a metamaterial that makes red light bounce backwards. As exciting as the prospect of an invisibility cloak might be, these breakthroughs are still only small steps in that direction. But this research could also have more short-term applications, like helping create DVDs that can hold many high definition movies and microscope-like instruments with incredible resolution.

New teachers are sometimes encouraged or required to attend a master teacher's class and observe. But a University of Michigan program gives teachers and those studying to become teachers a unique opportunity to immediately follow up their observation of the class with access to copies of student work, discussion with peers and education researchers, and questions to the master teacher. This program, says teacher and researcher Deborah Ball, seeks to answer a question, "What's the math you need to know to teach?" and in doing so "expose the myth people have that teaching elementary math is easy."

This model of a "laboratory/classroom" allows educators to test teaching techniques, develop curricula, and help teachers analyze teaching styles by watching them in action rather than reading about them in a book or hearing about them in a lecture. Classes are videotaped and student work is photocopied for future reference. The idea of a model open classroom is not new, and originated in Japan as a research tool. But the inclusion of both academics and in-service teachers in the discussion and analysis of model lessons may help bridge the gap between mathematicians' and classroom-teachers' visions of elementary education.

As more Americans opt for environmentally conscious "low-carbon diets", the need for skillful "dietary counseling" is emerging. Online calculators, some of which are designed by energy experts at leading universities, can estimate a users carbon footprint via answers to a survey and even prescribe changes in behavior to reach a lighter usage. Perhaps these calculators were used by some of the guilt-ridden Americans who spent $54 million last year on carbon off-sets (investments in carbon-reducing or carbon-capturing enterprises). But as of yet, no universal method or set of variables has yet been agreed upon for calculating the number of tons of carbon emitted due to an individual’s actions. Some online calculators include other greenhouse gasses with carbon, some take into consideration only the number of miles flown in a plane and not the number of flights or legs of the journey, some take into account the carbon used in producing a car as well as using it.

Different scales may give different readings, but some relationships are clear. The average American is responsible for four to five times the carbon emissions as the average human worldwide. Flying is far more of a carbon-monger than other forms of transportation. And being vegetarian can significantly decrease ones carbon footprint. So while we wait for the "instant carbon footprint" icon to pop up on our blackberries and ipods, we just have to remember to consult the same online calculator to track our progress towards zero carbon.

The Rubik's cube caught the world's attention in the 1970s. It also has fascinated mathematicians. This article talks about mathematicians' efforts to find the smallest number of moves needed to unscramble any Rubik's cube configuration---this number has been dubbed "God's number" by cube enthusiasts. The number of possible configurations is huge---43 billion billion, according to the article. Through an ingenious combination of group theory and computing power, mathematicians have been able to prove that God's number is 22 or less. Some Rubik's cube experts are convinced the bound is only 20, but a proof remains out of reach for now.

"'Kiss My Math' Tries to Make Pre-Algebra Cool": Interview with Danica KcKellar. Talk of the Nation, National Public Radio, 8 August 2008.

Actress-mathematician Danica McKellar has written a new book, Kiss My Math: Showing Pre-Algebra Who's Boss. Although the book is aimed at girls aged 12-14, she finds that middle school boys also read it. Her previous book, Math Doesn't Suck (see media coverage), was written for younger students who, she found while doing extensive research, find fractions a challenge. This new book focuses on integers, which McKellar's research showed to be the next stumbling block for students. She says she never imagined her first book would do so well (her publisher asked her to write another volume), and she receives emails from students on how helpful the books are. In both books she tries to address the problem of girls "dumbing themselves down" because they don't think being smart and being interested in math makes them attractive. McKellar cites the recent article in Science on the recent national report on math and gender that found that girls score as well as boys but that, she notes, "did not say [girls] are as interested in math and did not say they are going into math careers." She responds to some calls from the radio program listeners, addressing math education, math concepts, and her own experience in middle and high school. She reveals that she plans to write a third book, on algebra, but in the meantime plan to continue acting and promoting awareness of her books and math for young girls.

In this article, author Alexander Masters describes a portion of a three-week boat and train trip he took to the Arctic Circle last year with the subject of a future book: mathematician Simon Phillips Norton. Masters scheduled the trip, hoping to learn more about the typically reticent Norton and his work on the monster group. Norton was a mathematical prodigy who won a gold medal at the International Math Olympiad at the age of 15 and again at 16. Masters writes that "in his teens and twenties [Norton] was considered, potentially, the greatest British mathematician since Newton." These days, however, although Norton still publishes and gives talks, "the mania for mathematics has gone, like an illness," Masters notes.

During the trip, Masters does not learn much from Norton, a man Masters describes as having "no sense of anecdotes or extended conversation" and "no self-curiosity." Occasionally Norton speaks of mathematics, but he is easily distracted by hunger or with the need to identify his position on one of the maps he carries with him: "more than 10 minutes away from a map and he starts to feel he has lost his connection with the world." However, Masters does think of a subtitle for his book as he considers Norton's ready smile: "Simon Phillips Norton: The biography of a happy man."

Donald Berry, a biostatistician from the University of Texas, presents his case for why current doping tests for athletes shouldn't be the final determination of guilt. Berry explains that laboratory practices and diagnostic testing methods are imprecise and lack experimental data that would be required to determine a true false positive rate. He examines the probability that cyclist Floyd Landis, who lost his 2006 Tour de France win title due to doping charges, received a false positive based on the number of tests he took and multiple different false positive rates. Berry also explains how attorneys frequently miscalculate the odds of guilt based on the rarity of an event. He notes that bolstering the application of statistical and diagnostic rigor in doping tests will not be able to prove the innocence of defamed athletes like Landis, but will allow for better detection of true cheaters in the future.

PGA golfer Phil Mickelson and his wife Amy testified before a panel of the U.S. House of Representatives Labor and Education committee about efforts to improve math and science education. A professional golfer and his wife may not seem like experts in the subject but they have donated their time and money to the Mickelson ExxonMobil Teachers Academy, which has trained 1400 elementary school teachers in the last three years. The two told the committee about their academy, and Phil explained how he uses statistics to optimize his training time. (See also an April 2007 Math Digest about an ad campaign featuring Mickelson, that highlighted applications of mathematics.)

"Settling the Score," by Jason Turbow. Popular Science, August 2008, pages 66-70.

Many of the traditional statistics used to measure professional athletes' performance, such as batting average in baseball or points-per-game in basketball, are being refined by fans. This article talks about new sophisticated measures used in football, baseball, basketball, and hockey, as well as listing the top players according to the old and new statistics. One example involves the rating of quarterbacks in the National Football League. People seeking to improve the NFL's passer rating point out that it penalizes quarterbacks for throwing the ball away, rather than taking a sack (which has no impact on the rating but is almost always bad for the team). Also the passer rating scale is from 0 to 158.3, so it can be hard to judge the performance of a quarterback using the number (obviously a 158 is good, but what about a rating of 80?). Aaron Schatz has created the DVOA---defense-adjusted value over average---which uses yards gained in relation to how many yards are needed to get a first down. Other factors, such as big plays, are also part of this new statistic. It compares individuals to the league average, which is set at 0. The leader in DVOA last season (and passer rating) was Tom Brady, who had a DVOA of 57, which means that he was 57 percent better than the quarterback league average. Trent Dilfer and Alex Smith, both of the San Francisco 49ers, had the worst DVOAs, -52 and -49, respectively.